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Reserve tank 1 is capable of holding z gallons of water. Wat

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Reserve tank 1 is capable of holding z gallons of water. Wat [#permalink] New post 23 Jan 2008, 11:18
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56% (03:33) correct 44% (02:18) wrong based on 189 sessions
Reserve tank 1 is capable of holding z gallons of water. Water is pumped into tank 1, which starts off empty at a rate of x gallons per minute. Tank 1 simultaneously leaks water at a rate of y gallons per minute (x>y).The water that leaks out of tank 1 drips into tank 2,which also starts off empty. If the total capacity of tank 2 is twice the number of gallons that remains in tank 1 after 1 minute, does tank 1 fill up before tank 2?

(1) zy < 2x^2-4xy+2y^2
(2) Total capacity of tank 2 is less than one half that of tank 1.
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Jul 2013, 13:04, edited 1 time in total.
Edited the question.
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Re: DS - Tank [#permalink] New post 23 Jan 2008, 11:33
Expert's post
it seems to be A.
What is a source of question?
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Re: DS - Tank [#permalink] New post 23 Jan 2008, 11:52
Hi Walker,

The source is ManhattanGmat
Cuold you please detail a little how you reached the answer?

Thanks



walker wrote:
it seems to be A.
What is a source of question?
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Re: DS - Tank [#permalink] New post 23 Jan 2008, 12:29
capacity of tank 2 is u = 2*(x-y)

time it takes for tank 2 to get filled is 2*(x-y)/y
time it takes for tank 1 to get filled is z/(x-y)

z/(x-y) - 2*(x-y)/y < 0? equivalent (since y > 0 , x-y > 0)

zy < 2*(x-y)^2 = 2*x^2-4*x*y + 2*y^2 (1) is sufficient
2 is irrelevant
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Re: work_DS [#permalink] New post 13 Mar 2011, 23:44
I'd say A.

1 tells us that if Z was 100, x and y were 10 and 5 respectively, 1 would not be true. for 1 to be true, x and y will be 10 and 1 or around that area.

B tells us nothing about the rate at which water is flowing into the second tank.

Any other thoughts?
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Re: work_DS [#permalink] New post 14 Mar 2011, 00:15
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Time to fill tank 1= z/(x-y)
Tank 1 will be (x-y) full after 1 minute
Thus, capacity of "tank 2"=2(x-y)
Time to fill "tank 2"=2(x-y)/y

Q: is z/(x-y) < 2(x-y)/y
OR
is zy< 2 (x-y)^2

1. zy<2x^2-4xy+2y^2
zy< 2(x^2-2xy+y^2)
zy< 2(x-y)^2
Sufficient.

2. 2(x-y) < (1/2)z
4 < z/(x-y)
z/(x-y) > 4
But is;
z/(x-y) < 2(x-y)/y
Can't simplify any further.
Not sufficient.

Ans: "A"
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Re: work_DS [#permalink] New post 14 Mar 2011, 03:07
Another "lone wolf". Here the complex equation is A

Quote:
# The Lone Wolf

A lone wolf question almost always has a free standing number(or numbers), and a more complex looking equation as the other option. For e.g.

"On a loan, evil necromonger charges X% interest in the first year, and Y% interest in the second. If he loaned Rhyme 20,000$ in 2006, how much Rhyme pay by interest in 2008?"
A) X = 10
B) (X + Y + XY/100) = 100

You can almost be certain, that in such questions, your equations to the stem will reduce to a form that looks like (B), so (A) is actually redundant. Be careful of lone wolves because they will bite you in the posterior if you choose (C).

If you notice a lone wolf question, and you have no clue on how to solve the problem, choose (B) (or whichever is the complex equation).
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Re: DS Work Rate Problems [#permalink] New post 01 Oct 2011, 23:51
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After one minute there is y gallons in the tank 2, so the capacity of the tank 2 is 2(x-y) gallons.
Obviously, each minute the tank 1 is filled with x-y gallons of water, and tank 2 is filled with y gallons.

Let A is the number of minutes after which the 1 tank is full, and B is the number of minutes after which 2 the 2 tank is full.
Then:
A(x-y)=z
By=2(x-y)

A=\frac{z}{x-y}
B=\frac{2(x-y)}{y}

We need to compare A and B, so we are comparing \frac{z}{x-y} and \frac{2(x-y)}{y}

\frac{z}{x-y} ... \frac{2(x-y)}{y}
yz ... 2(x-y)(x-y)
yz ... 2x^2-4xy+2y^2

If (1) is true, then yz< 2x^2-4xy-y^2
Since 2x^2-4xy+2y^2> 2x^2-4xy-y^2, then yz <2x^2-4xy+2y^2 and we are able to compare two time periods. The statement (1) alone is susfficient.

If (2) is true, then 2(x-y)<0.5z
\frac{z}{x-y}>4
This means that A>4
However, B=\frac{2(x-y)}{y}, so there is no z and we only know that x>y, but nothing could be said to compare x-y and y. For example, if x=2y, then B=2 and A>B. However, if x=5y, then B=8 and we could not compare A and B.

So, the answer is (A)

NOTE: You should post DS problems in the other forum.
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Re: Reserve tank 1 is capable of holding z galllons of water [#permalink] New post 16 Dec 2011, 06:00
Nice problem. Got to the answer but took more than 3 mins... :( Problem statement itself took very long to read and understand
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Re: Reserve tank 1 is capable of holding z gallons of water. Wat [#permalink] New post 21 Jan 2014, 10:35
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Re: Reserve tank 1 is capable of holding z gallons of water. Wat   [#permalink] 21 Jan 2014, 10:35
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